So I was reading this scientific article and stumbled upon the following phrase:

"winL is a subset of partL also containing objects within epsilon of r."

It's refering to distances as shown in the picture below (the gray part is winL, which contains the objects positioned within epsilon meters of r).

What exactly does it mean? I'm not a native English speaker and I don't know how to explain this.

Later edit: So I figured out a better, less technical example, inspired from the first answer. What does within mean when you say: "x is within an arbitrarily small distance of r".

Ride like the wind


1 Answer 1


Epsilon just indicates an arbitrarily small value. It comes from the epsilon-delta technique used in mathematical analysis.

So, "within epsilon meters of r" just means "within an arbitrarily small distance of r". That is, the distance between p2 and p1 must not be less than r - ε or greater than r + ε.

This looks like something from perturbation theory.

  • Yes, but how do you explain "within an arbitrarily small distance of r"? Does that actually mean "positioned between r-epsilon and r+epsilon"?
    – Hello Lili
    Dec 3, 2016 at 17:33
  • @HelloLili See my edits.
    – Mick
    Dec 3, 2016 at 17:39

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